 ### Bayesian Knowledge Tracing

an explorable explainable
by Tongyu Zhou, Haoyu Sheng, Iris Howley

Bayesian knowledge tracing (BKT) is an AI algorithm used in intelligent tutoring systems to model a learner’s mastery of the skill being taught.

Let us first consider this algorithm (BKT) in the context of an “alchemy” metaphor. Think of the large beaker as representative of the overall mastery of the student for the one skill of interest. The test tubes are representative of the factors that go into calculating mastery.

These factors are called parameters. BKT uses a total of 4 different parameters. From left to right, they are:
1) init : probability of learner knowing the skill beforehand
2) transit : probability of learner learning the skill after application
3) slip : probability of learner messing up when using a known skill
4) guess : probability of learner has a lucky guess

The probabilities of these parameters ultimately affect mastery, which is the probability that a particular skill has been learned.

The weights these parameters carry in the equation are determined by the person applying the algorithm.

Slide the four values below to change the probability:
Init: 1.00 Transit: 1.00 Slip: 0.10 Guess: 0.30

P(slip) <= 0.1 and P(guess) <= 0.3 to make realistic predictions
When fitting parameters, we choose combinations that give the best sum-of-squares residual

Before taking the actual evaluation (or after pre-test), the probability of a student mastering the skill is equal to the init probability: The greater the value (the more the learner knows), the faster the gauge fills up (and the faster we reach full mastery)!

The algorithm relies on something called “conditional probability.” That is, depending on whether a learner answers a current question correctly or incorrectly, the formulas we use to calculate their mastery for that state will be different! Continuing with the notion of “conditional probability,” the mastery of a current state also depends on the mastery of a previous state. Try toggling the series of answers to see what happens when they are correct/incorrect. Mastery percentage growth rate:

x-axis: next x questions
y-axis: percentage increase

Note that even when a learner gets everything wrong, the mastery still increases, albeit by a little bit

The learner continues to answer questions...

Until?

they have answered as least one question
they have achieved at least 95% mastery
they have a streak of 10 correct answers
The skill is unmastered